math

4/14/23, 5:03 PM Sec. 12.4-Susy Rosales

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Student: Susy Rosales Date: 04/14/23

Instructor: Maria Montesdeoca Course: MGF 1106 MDC online Spring 2023 Assignment: Sec. 12.4

The scores on a test are normally distributed with a mean of and a standard deviation of . What is the score that is standard

the mean?

50 10 2 1 2

deviations above

A score of is standard the mean.2 1 2

deviations above

The scores on a test are normally distributed with a mean of and a standard deviation of . What is the score that is standard the mean?

90 18 2 deviations above

A score of is standard the mean.2 deviations above

The scores on a test are normally distributed with a mean of and a standard deviation of . Find the score that is standard

deviations above the mean.

150 30 1 1 2

A score of is standard deviations above the mean.1 1 2

The scores on a test are normally distributed with a mean of and a standard deviation of . What is the score that is standard the mean?

30 6 2 deviations below

A score of is standard the mean.2 deviations below

The scores on a test are normally distributed with a mean of and a standard deviation of . Find the score that is standard the mean.

80 16 one-half a deviation below

A score of is standard the mean.one-half a deviation below

Not everyone pays the same price for the same model of a car. The figure illustrates a normal distribution for the prices paid for a particular model of a new car. The mean is and the standard deviation is .

$20,000 $1000

Use the Rule to find what percentage of buyers paid between

and

68-95-99.7

$19,000 $21,000. Price of a Model of a New Car (Thousands)

20 21 22 23191817

The percentage of buyers who paid between and is $19,000 $21,000 %.

Not everyone pays the same price for the same model of a car. The figure illustrates a normal distribution for the prices paid for a particular model of a new car. The mean is and the standard deviation is .

$19,000 $2000

Use the Rule to find what percentage of buyers paid between

and

68-95-99.7

$15,000 $19,000. Price of a Model of a New Car (Thousands)

19 21 23 25171513

The percentage of buyers who paid between and is %.$15,000 $19,000 (Type an exact answer.)

4/14/23, 5:03 PM Sec. 12.4-Susy Rosales

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The figure illustrates a normal distribution for the prices paid for a particular model of a new car. The mean is and the standard deviation is

. $19,000

$500 Use the Rule to find the percentage of buyers who paid between

and

68-95-99.7

$17,500 $19,000.

Price of a Model of a New Car

What percentage of buyers paid between and ?$17,500 $19,000

%

The figure illustrates a normal distribution for the prices paid for a particular model of a new car. The mean is and the standard deviation is

. $12,000

$500 Use the Rule to find the percentage of buyers who paid between

and

68-95-99.7

$10,500 $12,000.

Price of a Model of a New Car

What percentage of buyers paid between and ?$10,500 $12,000

%

Not everyone pays the same price for the same model of a car. The figure illustrates a normal distribution for the prices paid for a particular model of a new car. The mean is and the standard deviation is . Use the Rule to find the percentage of buyers who paid

than .

$23,000 $2000 68-95-99.7

more $25,000

Price of a Model of a New Car (Thousands) 23 25 27 29211917

The percentage of buyers who paid than is more $25,000 %.

Not everyone pays the same price for the same model of a car. The figure illustrates a normal distribution for the prices paid for a particular model of a new car. The mean is and the standard deviation is . Use the

Rule to find the percentage of buyers who paid than .

$18,000 $1000

68-95-99.7 less $16,000

Price of a Model of a New Car (Thousands) 18 19 20 21171615

The percentage of buyers who paid than is less $16,000 %. (Type an integer or a decimal.)

Scores on the GRE (Graduate Record Examination) are normally distributed with a mean of and a standard deviation of . Use the Rule to find the percentage of people taking the test who score

583 80 68-95-99.7 between 503 and 663.

The percentage of people taking the test who score is between 503 and 663 %.

19,000 19,500 20,000 20,50018,50018,00017,500

12,000 12,500 13,000 13,50011,50011,00010,500

4/14/23, 5:03 PM Sec. 12.4-Susy Rosales

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Scores on the GRE (Graduate Record Examination) are normally distributed with a mean of and a standard deviation of . Use the Rule to find the percentage of people taking the test who score

558 74 68-95-99.7 between 484 and 558.

The percentage of people taking the test who score is between 484 and 558 %.

Scores on a standardized intelligence test are normally distributed with a mean of and a standard deviation of . Use the Rule to find the percentage of people taking the test who score

100 10 68-95-99.7 above 110.

The percentage of people taking the test who score is above 110 %. (Type an integer or a decimal.)

Scores on a standardized intelligence test are normally distributed with a mean of and a standard deviation of . Use the Rule to find the percentage of people taking the test who score

100 13 68-95-99.7 below 74.

The percentage of people taking the test who score is below 74 %. (Type an integer or a decimal.)

Scores on a standardized intelligence test are normally distributed with a mean of and a standard deviation of . Use the Rule to find the percentage of people taking the test who score

100 10 68-95-99.7 above 130.

The percentage of people taking the test who score is above 130 %. (Type an integer or a decimal.)

A set of data items is normally distributed with a mean of and a standard deviation of . Convert to a z-score.50 7 57

z57 = (Type an integer or a decimal.)

A set of data items is normally distributed with a mean of and a standard deviation of . Convert to a z-score.70 8 94

z94 = (Type an integer or a decimal.)

A set of data items is normally distributed with a mean of and a standard deviation of . Convert to a z-score.65 10 100

z100 = (Type an integer or a decimal.)

A set of data items is normally distributed with a mean of and a standard deviation of . Convert to a z-score.65 8 79

z79 = (Type an integer or a decimal.)

A set of data items is normally distributed with a mean of and a standard deviation of . Convert to a z-score.40 4 40

z40 = (Do not round until the final answer. Then round to the nearest hundredth as needed.)

A set of data items is normally distributed with a mean of and a standard deviation of . Convert to a z-score.55 5 45

z45 = (Type an integer or a decimal.)

A set of data items is normally distributed with a mean of and a standard deviation of . Convert to a z-score.70 6 61

z61 = (Type an integer or a decimal.)

4/14/23, 5:03 PM Sec. 12.4-Susy Rosales

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A set of data items is normally distributed with a mean of and a standard deviation of . Convert to a z-score.80 4 73

z73 = (Type an integer or a decimal.)

Scores on a dental anxiety scale range from 0 (no anxiety) to (extreme anxiety). The scores are normally distributed with a mean of and a standard deviation of . Find the z-score for the given score on this dental anxiety scale.

30 12 4

22

(Type an integer or a decimal.)z22 =

Scores on a dental anxiety scale range from 0 (no anxiety) to (extreme anxiety). The scores are normally distributed with a mean of and a standard deviation of . Find the z-score for the given score on this dental anxiety scale.

30 15 4

20

(Type an integer or a decimal.)z20 =

Scores on a dental anxiety scale range from 0 (no anxiety) to (extreme anxiety). The scores are normally distributed with a mean of and a standard deviation of . Find the z-score for the given score on this dental anxiety scale.

40 26 4

23

(Type an integer or a decimal.)z23 =

Scores on a dental anxiety scale range from 0 (no anxiety) to (extreme anxiety). The scores are normally distributed with a mean of and a standard deviation of . Find the z-score for the given score on this dental anxiety scale.

30 19 4

17

(Type an integer or a decimal.)z17 =

Intelligence quotas on two different tests are normally distributed. Test A has a mean of and a standard deviation of . Test B has a mean of 100 and a standard deviation of . Use z-scores to determine which person has the higher IQ: an individual who scores on Test A or an individual who scores on Test B.

100 12 13 120

129

Which individual has the higher IQ?

A. The individual who scores 129 on Test B.

B. The individual who scores 120 on Test A.

C. Both individuals have the same IQ.

A set of data items is normally distributed with a mean of and a standard deviation of . Find the data item in this distribution that corresponds to the given z-score.

900 10

z = 6

The data item that corresponds to is . (Type an integer or a decimal.)z = 6

A set of data items is normally distributed with a mean of and a standard deviation of . Find the data item in this distribution that corresponds to the given z-score.

100 30

z = 2.5

The data item that corresponds to z is . (Type an integer or a decimal.)= 2.5

4/14/23, 5:03 PM Sec. 12.4-Susy Rosales

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A set of data items is normally distributed with a mean of and a standard deviation of . Find the data item in this distribution that corresponds to the given z-score.

800 60

z = − 4

The data item that corresponds to is . (Type an integer or a decimal.)z = − 4

A set of data items is normally distributed with a mean of and a standard deviation of . Find the data item in this distribution that corresponds to the given z-score.

300 40

z = − 2.1

The data item that corresponds to is . z = − 2.1 (Type an integer or a decimal.)

The data in the accompanying bar graph are from a random sample of adults. The graph shows four proposals to reduce gun violence in a country and the percentage of surveyed adults who favored each of these proposals. Complete parts (a) and (b) below.

881

0

20

40

60

80

P er

ce nt

ag e

of A

du lts

F av

or in

g th

e P

ro po

sa l

Required gun registration

Ban on high-capacity magazines

Ban on assault weapons

Restrict amount or type of ammunition

purchases

60% 59% 57% 51%

a. Find the margin of error for this survey.

The margin of error is %.± (Do not round until the final answer. Then round to the nearest tenth as needed.)

b. Write a statement about the percentage of adults in the country's population who favor to reduce gun violence.

a ban on high-capacity magazines

There is 95% confidence that between % and % of all adults in the country favor .

a ban on high-capacity magazines (Use ascending order. Round to the nearest tenth as needed.)

Using a random sample of TV households, Acme Media Statistics found that watched the final episode of " " 1928 28.1% It Ain't Over Yet. a. Find the margin of error in this percent. b. Write a statement about the percentage of TV households in the population who tuned into the final episode of " " It Ain't Over Yet.

a. The margin of error is ± %. (Do not round until the final answer. Then round to the nearest hundredth as needed.)

b. Complete the following statement.

We can be 95% confident that between % and % of all households watched the final episode of " "It Ain't Over Yet. (Use ascending order. Round to the nearest hundredth as needed.)

Proposals to Reduce Gun Violence

4/14/23, 5:03 PM Sec. 12.4-Susy Rosales

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(1) greater than less than

approximately equal to

(2) skewed left. uniform. approximately normal. skewed right.

There are states in a certain country. The histogram shows murder rates per 100,000 residents and the number of states that had these rates in a certain year. Use this information to complete parts (a) through (e) to the right.

50

Murder Rates per 100,000 Residents, by State

0 1 2 3 4 5 6 7 8 9 10 11 12 13 0 1 2 3 4 5 6 7 8 9

10

Fr eq

ue nc

y

1 0

3 2

4 3

4

6

8 9

6

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a. Is the shape of this distribution best classified as normal, skewed left, or skewed right?

Choose the correct distribution type below.

A. Skewed right

B. Uniform distribution

C. Normal distribution

D. Skewed left

b. Calculate the mean murder rate per 100,000 residents for the states.

The mean murder rate is murders per 100,000 residents. (Type an integer or decimal rounded to two decimal place as needed.)

c. Find the median murder rate per 100,000 residents for the states.

The median murder rate is murders per 100,000 residents. (Type an integer or decimal rounded to one decimal place as needed.)

d. Are the mean and median murder rates consistent with the shape of the distribution that you described in part (a)? Explain your answer.

The mean is (1) the median. This is consistent

with the fact that the distribution given is (2)

e. Suppose there is a state with a rate of 29 murders per 100,000 residents. The standard deviation for the data is approximately

. If the distribution were roughly normal, what would be the z-score, rounded to one decimal place for that state? Use the same value for the mean that you found in part (b). Does this seem unusually high? Explain your answer.

4.7

The z-score is . (Type an integer or decimal rounded to one decimal place as needed.)

Choose the best explanation below.

A. The z-score is high, but it is expected that some values will be in the 3rd quartile.

B. This is unusually high. When modeling real phenomena, there can be anomalous data points which are not easily explained.

C. The z-score is too high. A state could not have that high of a rate.

Murder Rate (per 100,000 residents) Rounded to the Nearest Whole Number